Solution:-
From the given figure,
AB = AC. If PM ⊥ AB and PN ⊥ AC
We have to show that, PM x PC = PN x PB
Consider the ∆ABC,
AB = AC … [given]
∠B = ∠C
Then, consider ∆CPN and ∆BPM
∠N = ∠M … [both angles are equal to 90o]
∠C = ∠B … [from above]
Therefore, ∆CPN ~ ∆BPM … [from AA axiom]
So, PC/PB = PN/PM
By cross multiplication we get,
PC x PM = PN x PB
Therefore, it is proved that, PM x PC = PN x PB